Inference for systems of stochastic differential equations from discretely sampled data: A numerical maximum likelihood approach

Thomas Lux

No 1781, Kiel Working Papers from Kiel Institute for the World Economy (IfW Kiel)

Abstract: Maximum likelihood estimation of discretely observed diffusion processes is mostly hampered by the lack of a closed form solution of the transient density. It has recently been argued that a most generic remedy to this problem is the numerical solution of the pertinent Fokker-Planck (FP) or forward Kol- mogorov equation. Here we expand extant work on univariate diffusions to higher dimensions. We find that in the bivariate and trivariate cases, a numerical solution of the FP equation via alternating direction finite difference schemes yields results surprisingly close to exact maximum likelihood in a number of test cases. After providing evidence for the effciency of such a numerical approach, we illustrate its application for the estimation of a joint system of short-run and medium run investor sentiment and asset price dynamics using German stock market data.

Keywords: stochastic differential equations; numerical maximum likelihood; Fokker-Planck equation; finite difference schemes; asset pricing (search for similar items in EconPapers)
JEL-codes: C13 C58 G12 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2) Track citations by RSS feed

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/60335/1/720581907.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zbw:ifwkwp:1781

Access Statistics for this paper

More papers in Kiel Working Papers from Kiel Institute for the World Economy (IfW Kiel) Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().